I would have check/raise flop here and fold on his shove flop.
If i see the turn I value bet 1/2pot. I go broke easily on this board

Your bet sizing is quite nice, but you don't need to protect that much, the board is not THAT drawy. 0.20 and 0.50 was enough flop and turn imho. You want to be paid by weaker hand, not to make them fold, remember
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